Estimate the average power output of the sun, given that
about1350w/m2 reaches the upper atmosphere of theearth.
this distance from the sun to the earth is 1.5
x1011m.

Intensity is defined to be the power per unit area carried by a wave. Power is the rate at which energy is transferred by the wave. In equation form, intensity I is

I=\frac{P}{A}

Where P is the power through an area A.  

Rearranging to find the Power we have that,

P = IA

The value of the given area for land can be approximated to that of a sphere, therefore the Area would be equivalent to

Where r represents the distance from the sun to the earth.

Replacing with our values we have that

Therefore the average power output of the sun is

where are the vectors ?